Making a claim of self-defense means you will have to show evidence of the crime committed against you -- the one that made it necessary for you to shoot.

If the responding officers do not hear about that crime, they won't investigate it or look for evidence that it happened.

Without evidence of the crime committed against you, you'll have a much harder time defending your use of deadly force. "Self-defense" falls down as a claim if there wasn't anything for you to defend against.

Be a good witness. Tell the arriving officers there was a crime committed against you. Point out evidence and witnesses. Then shut up.